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Register a new userThe underlying physical meaning of the $ u_{rm max}- u_{rm c}$ relation
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Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($ u_{rm max}$) of solar-like oscillations and the cut-off frequency ($ u_{rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $ u_{rm max}$ and $ u_{rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.
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Scaling relations between asteroseismic quantities and stellar parameters are essential tools for studying stellar structure and evolution. We will address two of them, namely, the relation between the large frequency separation ($Delta u$) and the mean density ($bar{rho}$) as well as the relation between the frequency of the maximum in the power spectrum of solar-like oscillations ($ u_{rm max}$) and the cut-off frequency ($ u_{rm c}$). For the first relation, we will consider the possible sources of uncertainties and explore them with the help of a grid of stellar models. For the second one, we will show that the basic physical picture is understood and that departure from the observed relation arises from the complexity of non-adiabatic processes involving time-dependent treatment of convection. This will be further discussed on the basis of a set of 3D hydrodynamical simulation of surface convection.
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By analyzing 482 pb$^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy $sqrt s=4.009$ GeV with the BESIII detector, we measure the %absolute branching fractions for the semi-leptonic decays $D_{s}^{+}to phi e^{+} u_{e}$, $phi mu^{+} u_{mu}$, $eta mu^{+} u_{mu}$ and $etamu^{+} u_{mu}$ to be ${mathcal B}(D_{s}^{+}tophi e^{+} u_{e})=(2.26pm0.45pm0.09)$%, ${mathcal B}(D_{s}^{+}tophi mu^{+} u_{mu})=(1.94pm0.53pm0.09)$%, ${mathcal B}(D_{s}^{+}toeta mu^{+} u_{mu})=(2.42pm0.46pm0.11)$% and ${mathcal B}(D_{s}^{+}toetamu^{+} u_{mu}) = (1.06pm0.54pm0.07)$%, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions for the three semi-muonic decays $D_s^+tophi mu^+ u_mu, eta mu^+ u_mu$ and $eta mu^+ u_mu$ are determined for the first time and that of $D^+_sto phi e^+ u_e$ is consistent with the world average value within uncertainties.
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